MA101: Single-Variable Calculus I

Unit 3: Rules for Finding DerivativesComputing a derivative requires computing a limit. Because limit
computations can be rather involved, we like to minimize the amount of
work we have to do in practice. In this unit, you will build your skill
using some rules for differentiation which will speed up your
calculations of derivatives. In particular, you will see how to
differentiate the sum, difference, product, quotient, and composition of
two or more functions. You will also learn rules for differentiating
power functions, including polynomial and root functions.

Unit 3 Time Advisory
This unit should take you approximately 12 hours to complete.

☐ Subunit 3.1: 1 hour

☐ Subunit 3.2: 1.5 hours

☐ Subunit 3.3: 2 hours

☐ Subunit 3.4: 2.5 hours

☐ Subunit 3.5: 5 hours
☐ Reading: 1 hour

☐ Lecture: 1 hour

☐ Assignment: 3 hours

Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Use the power, product, quotient, and chain rules to calculate
derivatives.

Instructions: Please click on the link above and read Section 3.1
(pages 55-57) in its entirety. This section will show you a simple
rule for how to find the derivative of a power function without
explicitly computing a limit.

This reading should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the above link and work through
problems 1-6. When you are done, check your answers
against “Appendix A:
Answers”.

This assignment should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here. (PDF)

Instructions: Please click on the link above and read Section 3.2
(pages 58-59) in its entirety. In this reading, you will see how
the derivative behaves with regards to addition and subtraction of
functions and with scalar multiplication. That is, you will see
that the derivative is a linear operation.

This reading should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here. (PDF)

Instructions: Please click on the link above and work through
problems 1-9, 11, and 12. When you are done, check your
answers “Appendix A:
Answers”.

This assignment should take you approximately one hour to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the link above and read Section 3.3
(pages 60-61) in its entirety. The naïve assumption is that the
derivative of a product of two functions is the product of the
derivatives of the two functions. This assumption is false. In
this reading, you will see that the derivative of a product is
slightly more complicated, but that it follows a definite rule
called the product rule.

This reading should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here. (PDF)

Instructions: Please click on the link above and work through
problems 1-5. When you are done, check your answers
against “Appendix A:
Answers”.

This assignment should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the link above and select the
“Index.” Click on the number 44 next to “Product Rule” to launch
the module and complete problems 1-10. If at any time the problem
set becomes too easy for you, feel free to move forward.

This assignment should take you approximately one hour to
complete.

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

Instructions: Please click on the link above and select the
"Index." Click on the number 45 next to "The Quotient Rule" to
launch the module and complete problems 1-10. If at any time the
problem set becomes too easy for you, feel free to move forward.
This assignment should take you approximately one hour to
complete.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

Instructions: Please click on the link above and read Section 3.4
(pages 62-65) in its entirety. As with product of two functions,
the derivative of a quotient of two functions is not simply the
quotient of the two derivatives. This reading will introduce you to
the quotient rule for differentiating a quotient of two functions.
In particular, it will allow you to find the derivative of any
rational function.

This reading should take you approximately one hour to complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the link above and work through
problems 5, 6, 8, and 9. When you are done, check your answers
against “Appendix A:
Answers”.

This assignment should take you approximately 30 minutes to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the link above and read Section 3.5
(pages 65-69) in its entirety. The chain rule explains how the
derivative applies to the composition of functions. Pay particular
attention to Example 3.11, which works through a derivative
computation where all of the differentiation rules of this unit are
applied in finding the derivative of one function.

This reading should take you approximately one hour to complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.

Instructions: Please click on the link above and work through
problems 1-20 and 36-39. When you are done, check your answers
against “Appendix A:
Answers”.

This assignment should take you approximately three hours to
complete.

Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.